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Grips will not wrap the brake levers.
You have several options:
Find a compatible brake lever which has plastic levers
Wrap the brake levers in something (a few layers of heat shrink tubing, plasti-dip, a bit of plastic/vinyl tubing like you get for refrigerator water hoses, brake lever covers (they exist for motorcycles, so I suspect you can find them ...

It is a little hard to tell from your photos, but do you have grip shifters?
For setups with grip shifters, the grips are generally much shorter / narrower, as part of the "grip surface" is the shifter itself.
If you do indeed have grip shifters, you can do as ojs suggested & move the shifters / brakes in towards the stem, or, you could return the ...

You can move the brake and shift levers inward. They are tightened around the handlebar with hex bolts or screws, you can loosen these and move the parts around. If the result feels too narrow, you can change to a wider handlebar.
Edit: See the other answer for solution with grip shifters.

A razor blade/knife/x-acto knife should cut it. Hockey shops have special knifes for cutting through hockey tape if you want a specialized device. This shouldn't be a problem for non-carbon bars though, if you're careful.
The residue can be removed with rubbing alcohol or soapy water or mineral spirits (again, for carbon, I'm not sure what you'd do).

You need to check with the manufacturer of your bars (and the grips you're choosing), but in most cases its not a problem. As with all things carbon fiber, don't over tighten anything.
Some manufacturers have specific grips which are marketed as carbon fiber friendly. For example, Easton's lock on grips are marketed as being friendly with carbon bars.
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